On sl3 Knizhnik-Zamolodchikov equations and W3 null-vector equations
arXiv:0811.4587 · doi:10.1088/1126-6708/2009/10/002
Abstract
Starting from Sklyanin's separation of variables for the sl3 Yangian model, we derive the separation of variables for the quantum sl3 Gaudin model. We use the resulting new variables for rewriting the sl3 Knizhnik-Zamolodchikov equations, and comparing them with certain null-vector equations in conformal field theories with W3-algebra symmetry. The two sets of equations are remarkably similar, but become identical only in the critical level limit. This is in contrast to the sl2 Knizhnik-Zamolodchikov equations, which are known to be equivalent to Belavin-Polyakov-Zamolodchikov equations for all values of the level.
28 pages, v2: added a study of the minisuperspace limit; sections 3.3, 4.4 and 5 modified
References in corpus (7)
- Correlation functions in conformal Toda field theory I
- H^+_3 WZNW model from Liouville field theory
- On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model
- The FZZ-Duality Conjecture - A Proof
- Solution of the H3+ model on a disc
- A family of solvable non-rational conformal field theories
- A twisted FZZ-like dual for the two-dimensional black hole
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